From Chains to DAGs: Probing the Graph Structure of Reasoning in LLMs

TL;DR

This paper introduces a framework to analyze whether large language models internally encode reasoning as directed acyclic graphs, revealing that such graph structures are present and vary across layers and model scales.

Contribution

The authors propose Reasoning DAG Probing, a novel method to detect and analyze graph-structured reasoning in LLMs' internal representations.

Findings

DAG structure is meaningfully encoded in LLM representations.

Recoverability of reasoning graphs peaks in intermediate layers.

Graph structure varies systematically with node depth, edge span, and model scale.

Abstract

Recent progress in large language models has renewed interest in how multi-step reasoning is represented internally. While prior work often treats reasoning as a linear chain, many reasoning problems are more naturally modeled as directed acyclic graphs (DAGs), where intermediate conclusions branch, merge, and are reused. Whether such graph structure is reflected in model internals remains unclear. We introduce Reasoning DAG Probing, a framework for testing whether LLM hidden states linearly encode properties of an underlying reasoning DAG and where this structure emerges across layers. We associate each reasoning node with a textual realization and train lightweight probes to predict node depth, pairwise distance, and adjacency from hidden states. Using these probes, we analyze the emergence of DAG structure across layers, reconstruct approximate reasoning graphs, and evaluate controls that disrupt reasoning-relevant structure while preserving surface text. Across reasoning benchmarks, we find that DAG structure is meaningfully encoded in LLM representations, with recoverability peaking in intermediate layers, varying systematically by node depth, edge span, and model scale, and enabling nontrivial recovery of dependency graphs. These findings suggest that LLM reasoning is not purely sequential, but exhibits measurable internal graph structure.